Two slabs A and B of equal surface area are placed one over the other such that their surfaces are completely in contact. The thickness of slab A is twice that of B. The coefficient of thermal conductivity of slab A is twice that of B. The first surface of slab A is maintained at \(100^{\circ}\mathrm{C}\) while the second surface of slab B is maintained at \(25^{\circ}\mathrm{C}\). The temperature at the common surface will be:
1. \(62.5^{\circ}\mathrm{C}\)
2. \(45^{\circ}\mathrm{C}\)
3. \(55^{\circ}\mathrm{C}\)
4. \(85^{\circ}\mathrm{C}\)
Two rods, one made of aluminium and the other made of steel, having initial lengths \(l_1\) and \(l_2\) are connected together to form a single rod of length . The coefficient of linear expansion for aluminium and steel are and respectively. If the length of each rod increases by the same amount when their temperature is raised by \(t^\circ \mathrm{C},\) then the ratio \(\frac{l_1}{l_1+l_2}\) is:
1.
2.
3.
4.
Three rods made of the same material and having the same cross-section have been joined as shown in the figure. Each rod has the same length. The left and right ends are kept at \(0^{\circ}\text{C}~\text{and}~90^{\circ}\text{C},\) respectively. The temperature at the junction of the three rods will be:
1. \(45^{\circ}\text{C}\)
2. \(60^{\circ}\text{C}\)
3. \(30^{\circ}\text{C}\)
4. \(20^{\circ}\text{C}\)
The rate of heat emission from an ideal black body at temperature T is H. What will be the rate of emission of heat by another body of same size at temperature 2T and emissivity 0.25?
1. | 16 H | 2. | 4 H |
3. | 8 H | 4. | 4.5 H |
\(150\) g of ice at \(0^\circ \mathrm{C}\) is mixed with \(100\) g of water at a temperature of \(80^\circ \mathrm{C}.\) The latent heat of ice is \(80\) cal/g and the specific heat of water is \(1\) cal/g°C. Assuming no heat loss to the environment, the amount of ice that does not melt is:
1. | \(100\) g | 2. | \(0\) |
3. | \(150\) g | 4. | \(50\) g |
Hot coffee in a mug cools from \(90^{\circ}\mathrm{C}\) to \(70^{\circ}\mathrm{C}\) in 4.8 minutes. The room temperature is \(20^{\circ}\mathrm{C}\). Applying Newton's law of cooling, the time needed to cool it further by \(10^{\circ}\mathrm{C}\) should be nearly:
1. | 4.2 minute | 2. | 3.8 minute |
3. | 3.2 minute | 4. | 2.4 minute |
One kilogram of ice at \(0^\circ \mathrm{C}\) is mixed with one kilogram of water at \(80^\circ \mathrm{C}.\) The final temperature of the mixture will be: (Take: Specific heat of water = \(4200\) J kg-1 K-1, latent heat of ice\(=336\) kJ kg-1)
1. | \(0^\circ \mathrm{C}\) | 2. | \(50^\circ \mathrm{C}\) |
3. | \(40^\circ \mathrm{C}\) | 4. | \(60^\circ \mathrm{C}\) |
Two identical bodies are made of a material whose heat capacity increases with temperature. One of these is at \(100^{\circ} \mathrm{C}\), while the other one is at \(0^{\circ} \mathrm{C}\). If the two bodies are brought into contact, then assuming no heat loss, the final common temperature will be:
1. | \(50^{\circ} \mathrm{C}\) |
2. | more than \(50^{\circ} \mathrm{C}\) |
3. | less than \(50^{\circ} \mathrm{C}\) but greater than \(0^{\circ} \mathrm{C}\) |
4. | \(0^{\circ} \mathrm{C}\) |
The value of the coefficient of volume expansion of glycerin is \(5\times10^{-4}\) K-1. The fractional change in the density of glycerin for a temperature increase of \(40^\circ \mathrm{C}\) will be:
1. | \(0.015\) | 2. | \(0.020\) |
3. | \(0.025\) | 4. | \(0.010\) |
Steam at \(100^{\circ}\mathrm{C}\) is injected into 20 g of \(10^{\circ}\mathrm{C}\) water. When water acquires a temperature of \(80^{\circ}\mathrm{C}\), the mass of water present will be: (Take specific heat of water =1 cal g-1 \(^\circ\)C-1 and latent heat of steam = 540 cal g-1)
1. | 24 g | 2. | 31.5g |
3. | 42.5 g | 4. | 22.5 g |